Properties

Label 360.2.bm.b.11.15
Level $360$
Weight $2$
Character 360.11
Analytic conductor $2.875$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [360,2,Mod(11,360)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(360, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("360.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 360.bm (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.87461447277\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 11.15
Character \(\chi\) \(=\) 360.11
Dual form 360.2.bm.b.131.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.475189 + 1.33199i) q^{2} +(-1.73205 + 0.00397907i) q^{3} +(-1.54839 + 1.26589i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.828349 - 2.30518i) q^{6} +(-2.40441 - 1.38819i) q^{7} +(-2.42193 - 1.46090i) q^{8} +(2.99997 - 0.0137839i) q^{9} +O(q^{10})\) \(q+(0.475189 + 1.33199i) q^{2} +(-1.73205 + 0.00397907i) q^{3} +(-1.54839 + 1.26589i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.828349 - 2.30518i) q^{6} +(-2.40441 - 1.38819i) q^{7} +(-2.42193 - 1.46090i) q^{8} +(2.99997 - 0.0137839i) q^{9} +(-0.915942 + 1.07752i) q^{10} +(-2.70422 - 1.56128i) q^{11} +(2.67685 - 2.19875i) q^{12} +(-3.30414 + 1.90765i) q^{13} +(0.706502 - 3.86230i) q^{14} +(-0.869469 - 1.49801i) q^{15} +(0.795033 - 3.92019i) q^{16} -3.43533i q^{17} +(1.44391 + 3.98938i) q^{18} +1.31386 q^{19} +(-1.87049 - 0.708000i) q^{20} +(4.17007 + 2.39484i) q^{21} +(0.794596 - 4.34389i) q^{22} +(-2.13186 - 3.69249i) q^{23} +(4.20071 + 2.52072i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-4.11106 - 3.49459i) q^{26} +(-5.19603 + 0.0358114i) q^{27} +(5.48026 - 0.894268i) q^{28} +(-0.266702 + 0.461941i) q^{29} +(1.58217 - 1.86996i) q^{30} +(0.413107 - 0.238507i) q^{31} +(5.59945 - 0.803857i) q^{32} +(4.69004 + 2.69345i) q^{33} +(4.57582 - 1.63243i) q^{34} -2.77637i q^{35} +(-4.62768 + 3.81898i) q^{36} -2.26255i q^{37} +(0.624333 + 1.75005i) q^{38} +(5.71534 - 3.31728i) q^{39} +(0.0542127 - 2.82791i) q^{40} +(-9.97758 + 5.76056i) q^{41} +(-1.20833 + 6.69249i) q^{42} +(-6.25878 + 10.8405i) q^{43} +(6.16360 - 1.00577i) q^{44} +(1.51192 + 2.59116i) q^{45} +(3.90532 - 4.59424i) q^{46} +(1.52710 - 2.64501i) q^{47} +(-1.36143 + 6.79312i) q^{48} +(0.354125 + 0.613362i) q^{49} +(-1.39113 - 0.254469i) q^{50} +(0.0136694 + 5.95014i) q^{51} +(2.70123 - 7.13648i) q^{52} -14.2847 q^{53} +(-2.51679 - 6.90404i) q^{54} -3.12256i q^{55} +(3.79531 + 6.87471i) q^{56} +(-2.27567 + 0.00522795i) q^{57} +(-0.742034 - 0.135735i) q^{58} +(-8.89170 + 5.13363i) q^{59} +(3.24259 + 1.21885i) q^{60} +(10.7109 + 6.18395i) q^{61} +(0.513993 + 0.436918i) q^{62} +(-7.23229 - 4.13137i) q^{63} +(3.73152 + 7.07642i) q^{64} +(-3.30414 - 1.90765i) q^{65} +(-1.35899 + 7.52698i) q^{66} +(3.47947 + 6.02663i) q^{67} +(4.34875 + 5.31923i) q^{68} +(3.70717 + 6.38708i) q^{69} +(3.69810 - 1.31930i) q^{70} +7.88557 q^{71} +(-7.28586 - 4.34928i) q^{72} +7.92558 q^{73} +(3.01369 - 1.07514i) q^{74} +(0.862577 - 1.50199i) q^{75} +(-2.03437 + 1.66321i) q^{76} +(4.33470 + 7.50792i) q^{77} +(7.13445 + 6.03644i) q^{78} +(0.187206 + 0.108084i) q^{79} +(3.79250 - 1.27158i) q^{80} +(8.99962 - 0.0827023i) q^{81} +(-12.4142 - 10.5527i) q^{82} +(-7.86428 - 4.54044i) q^{83} +(-9.48851 + 1.57072i) q^{84} +(2.97508 - 1.71766i) q^{85} +(-17.4136 - 3.18533i) q^{86} +(0.460102 - 0.801164i) q^{87} +(4.26855 + 7.73192i) q^{88} -4.82215i q^{89} +(-2.73295 + 3.24515i) q^{90} +10.5927 q^{91} +(7.97525 + 3.01871i) q^{92} +(-0.714571 + 0.414750i) q^{93} +(4.24878 + 0.777198i) q^{94} +(0.656931 + 1.13784i) q^{95} +(-9.69530 + 1.41460i) q^{96} +(-4.20125 + 7.27679i) q^{97} +(-0.648716 + 0.763153i) q^{98} +(-8.13409 - 4.64652i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 24 q^{5} - q^{6} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 24 q^{5} - q^{6} + 6 q^{8} + 13 q^{12} + 15 q^{14} - 12 q^{16} + 7 q^{18} + 4 q^{21} - 21 q^{22} - 4 q^{24} - 24 q^{25} + 12 q^{27} - 2 q^{30} - 8 q^{33} - 27 q^{34} - 31 q^{36} - 27 q^{38} - 16 q^{39} + 12 q^{40} + 12 q^{41} - 9 q^{42} + 24 q^{44} - 6 q^{46} - 12 q^{47} + 7 q^{48} + 24 q^{49} - 20 q^{51} + 54 q^{52} - 32 q^{54} + 21 q^{56} + 4 q^{57} + 33 q^{58} - 36 q^{59} - q^{60} - 12 q^{61} - 42 q^{62} - 56 q^{63} - 12 q^{64} - 32 q^{66} + 51 q^{68} + 40 q^{69} + 15 q^{70} + 6 q^{72} + 54 q^{74} - 51 q^{76} - 24 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} + 41 q^{84} + 27 q^{86} - 36 q^{87} - 57 q^{88} - 22 q^{90} - 9 q^{92} - 75 q^{94} + 13 q^{96} - 42 q^{98} - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(217\) \(271\) \(281\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.475189 + 1.33199i 0.336009 + 0.941859i
\(3\) −1.73205 + 0.00397907i −0.999997 + 0.00229732i
\(4\) −1.54839 + 1.26589i −0.774196 + 0.632946i
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) −0.828349 2.30518i −0.338172 0.941084i
\(7\) −2.40441 1.38819i −0.908782 0.524685i −0.0287426 0.999587i \(-0.509150\pi\)
−0.880039 + 0.474902i \(0.842484\pi\)
\(8\) −2.42193 1.46090i −0.856283 0.516507i
\(9\) 2.99997 0.0137839i 0.999989 0.00459462i
\(10\) −0.915942 + 1.07752i −0.289646 + 0.340742i
\(11\) −2.70422 1.56128i −0.815352 0.470744i 0.0334589 0.999440i \(-0.489348\pi\)
−0.848811 + 0.528696i \(0.822681\pi\)
\(12\) 2.67685 2.19875i 0.772740 0.634723i
\(13\) −3.30414 + 1.90765i −0.916405 + 0.529086i −0.882486 0.470338i \(-0.844132\pi\)
−0.0339183 + 0.999425i \(0.510799\pi\)
\(14\) 0.706502 3.86230i 0.188821 1.03224i
\(15\) −0.869469 1.49801i −0.224496 0.386784i
\(16\) 0.795033 3.92019i 0.198758 0.980049i
\(17\) 3.43533i 0.833189i −0.909092 0.416594i \(-0.863224\pi\)
0.909092 0.416594i \(-0.136776\pi\)
\(18\) 1.44391 + 3.98938i 0.340333 + 0.940305i
\(19\) 1.31386 0.301421 0.150710 0.988578i \(-0.451844\pi\)
0.150710 + 0.988578i \(0.451844\pi\)
\(20\) −1.87049 0.708000i −0.418254 0.158314i
\(21\) 4.17007 + 2.39484i 0.909984 + 0.522596i
\(22\) 0.794596 4.34389i 0.169408 0.926121i
\(23\) −2.13186 3.69249i −0.444524 0.769937i 0.553495 0.832852i \(-0.313294\pi\)
−0.998019 + 0.0629149i \(0.979960\pi\)
\(24\) 4.20071 + 2.52072i 0.857467 + 0.514539i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −4.11106 3.49459i −0.806245 0.685346i
\(27\) −5.19603 + 0.0358114i −0.999976 + 0.00689190i
\(28\) 5.48026 0.894268i 1.03567 0.169001i
\(29\) −0.266702 + 0.461941i −0.0495253 + 0.0857803i −0.889725 0.456496i \(-0.849104\pi\)
0.840200 + 0.542277i \(0.182437\pi\)
\(30\) 1.58217 1.86996i 0.288863 0.341406i
\(31\) 0.413107 0.238507i 0.0741962 0.0428372i −0.462443 0.886649i \(-0.653027\pi\)
0.536639 + 0.843812i \(0.319694\pi\)
\(32\) 5.59945 0.803857i 0.989852 0.142103i
\(33\) 4.69004 + 2.69345i 0.816431 + 0.468869i
\(34\) 4.57582 1.63243i 0.784746 0.279959i
\(35\) 2.77637i 0.469293i
\(36\) −4.62768 + 3.81898i −0.771279 + 0.636497i
\(37\) 2.26255i 0.371960i −0.982554 0.185980i \(-0.940454\pi\)
0.982554 0.185980i \(-0.0595460\pi\)
\(38\) 0.624333 + 1.75005i 0.101280 + 0.283896i
\(39\) 5.71534 3.31728i 0.915187 0.531190i
\(40\) 0.0542127 2.82791i 0.00857178 0.447131i
\(41\) −9.97758 + 5.76056i −1.55824 + 0.899648i −0.560809 + 0.827945i \(0.689510\pi\)
−0.997426 + 0.0717028i \(0.977157\pi\)
\(42\) −1.20833 + 6.69249i −0.186449 + 1.03267i
\(43\) −6.25878 + 10.8405i −0.954454 + 1.65316i −0.218842 + 0.975760i \(0.570228\pi\)
−0.735612 + 0.677403i \(0.763105\pi\)
\(44\) 6.16360 1.00577i 0.929198 0.151626i
\(45\) 1.51192 + 2.59116i 0.225384 + 0.386267i
\(46\) 3.90532 4.59424i 0.575808 0.677384i
\(47\) 1.52710 2.64501i 0.222750 0.385814i −0.732892 0.680345i \(-0.761830\pi\)
0.955642 + 0.294531i \(0.0951634\pi\)
\(48\) −1.36143 + 6.79312i −0.196506 + 0.980503i
\(49\) 0.354125 + 0.613362i 0.0505892 + 0.0876231i
\(50\) −1.39113 0.254469i −0.196736 0.0359874i
\(51\) 0.0136694 + 5.95014i 0.00191410 + 0.833187i
\(52\) 2.70123 7.13648i 0.374593 0.989651i
\(53\) −14.2847 −1.96215 −0.981075 0.193629i \(-0.937974\pi\)
−0.981075 + 0.193629i \(0.937974\pi\)
\(54\) −2.51679 6.90404i −0.342492 0.939521i
\(55\) 3.12256i 0.421046i
\(56\) 3.79531 + 6.87471i 0.507170 + 0.918671i
\(57\) −2.27567 + 0.00522795i −0.301420 + 0.000692459i
\(58\) −0.742034 0.135735i −0.0974338 0.0178228i
\(59\) −8.89170 + 5.13363i −1.15760 + 0.668341i −0.950728 0.310026i \(-0.899662\pi\)
−0.206873 + 0.978368i \(0.566329\pi\)
\(60\) 3.24259 + 1.21885i 0.418617 + 0.157352i
\(61\) 10.7109 + 6.18395i 1.37139 + 0.791774i 0.991103 0.133094i \(-0.0424913\pi\)
0.380289 + 0.924868i \(0.375825\pi\)
\(62\) 0.513993 + 0.436918i 0.0652772 + 0.0554886i
\(63\) −7.23229 4.13137i −0.911183 0.520504i
\(64\) 3.73152 + 7.07642i 0.466440 + 0.884553i
\(65\) −3.30414 1.90765i −0.409829 0.236615i
\(66\) −1.35899 + 7.52698i −0.167280 + 0.926507i
\(67\) 3.47947 + 6.02663i 0.425086 + 0.736270i 0.996428 0.0844417i \(-0.0269107\pi\)
−0.571343 + 0.820711i \(0.693577\pi\)
\(68\) 4.34875 + 5.31923i 0.527364 + 0.645051i
\(69\) 3.70717 + 6.38708i 0.446291 + 0.768914i
\(70\) 3.69810 1.31930i 0.442007 0.157687i
\(71\) 7.88557 0.935845 0.467922 0.883770i \(-0.345003\pi\)
0.467922 + 0.883770i \(0.345003\pi\)
\(72\) −7.28586 4.34928i −0.858647 0.512568i
\(73\) 7.92558 0.927620 0.463810 0.885935i \(-0.346482\pi\)
0.463810 + 0.885935i \(0.346482\pi\)
\(74\) 3.01369 1.07514i 0.350334 0.124982i
\(75\) 0.862577 1.50199i 0.0996018 0.173434i
\(76\) −2.03437 + 1.66321i −0.233359 + 0.190783i
\(77\) 4.33470 + 7.50792i 0.493985 + 0.855606i
\(78\) 7.13445 + 6.03644i 0.807817 + 0.683492i
\(79\) 0.187206 + 0.108084i 0.0210624 + 0.0121604i 0.510494 0.859881i \(-0.329462\pi\)
−0.489432 + 0.872042i \(0.662796\pi\)
\(80\) 3.79250 1.27158i 0.424015 0.142167i
\(81\) 8.99962 0.0827023i 0.999958 0.00918915i
\(82\) −12.4142 10.5527i −1.37092 1.16535i
\(83\) −7.86428 4.54044i −0.863217 0.498378i 0.00187155 0.999998i \(-0.499404\pi\)
−0.865088 + 0.501620i \(0.832738\pi\)
\(84\) −9.48851 + 1.57072i −1.03528 + 0.171380i
\(85\) 2.97508 1.71766i 0.322693 0.186307i
\(86\) −17.4136 3.18533i −1.87775 0.343483i
\(87\) 0.460102 0.801164i 0.0493281 0.0858938i
\(88\) 4.26855 + 7.73192i 0.455029 + 0.824225i
\(89\) 4.82215i 0.511147i −0.966790 0.255573i \(-0.917736\pi\)
0.966790 0.255573i \(-0.0822642\pi\)
\(90\) −2.73295 + 3.24515i −0.288078 + 0.342069i
\(91\) 10.5927 1.11042
\(92\) 7.97525 + 3.01871i 0.831477 + 0.314723i
\(93\) −0.714571 + 0.414750i −0.0740976 + 0.0430075i
\(94\) 4.24878 + 0.777198i 0.438228 + 0.0801618i
\(95\) 0.656931 + 1.13784i 0.0673997 + 0.116740i
\(96\) −9.69530 + 1.41460i −0.989523 + 0.144377i
\(97\) −4.20125 + 7.27679i −0.426573 + 0.738846i −0.996566 0.0828038i \(-0.973613\pi\)
0.569993 + 0.821649i \(0.306946\pi\)
\(98\) −0.648716 + 0.763153i −0.0655302 + 0.0770901i
\(99\) −8.13409 4.64652i −0.817506 0.466993i
\(100\) −0.322099 1.97389i −0.0322099 0.197389i
\(101\) 1.11068 1.92376i 0.110517 0.191421i −0.805462 0.592648i \(-0.798083\pi\)
0.915979 + 0.401227i \(0.131416\pi\)
\(102\) −7.91903 + 2.84565i −0.784101 + 0.281761i
\(103\) −12.7933 + 7.38623i −1.26056 + 0.727786i −0.973183 0.230030i \(-0.926117\pi\)
−0.287380 + 0.957817i \(0.592784\pi\)
\(104\) 10.7893 + 0.206838i 1.05798 + 0.0202821i
\(105\) 0.0110474 + 4.80881i 0.00107811 + 0.469292i
\(106\) −6.78791 19.0270i −0.659300 1.84807i
\(107\) 14.0755i 1.36073i −0.732872 0.680367i \(-0.761820\pi\)
0.732872 0.680367i \(-0.238180\pi\)
\(108\) 8.00015 6.63306i 0.769815 0.638267i
\(109\) 16.5073i 1.58111i −0.612389 0.790557i \(-0.709791\pi\)
0.612389 0.790557i \(-0.290209\pi\)
\(110\) 4.15922 1.48381i 0.396566 0.141475i
\(111\) 0.00900283 + 3.91883i 0.000854511 + 0.371959i
\(112\) −7.35355 + 8.32210i −0.694845 + 0.786365i
\(113\) 0.459459 0.265268i 0.0432222 0.0249544i −0.478233 0.878233i \(-0.658723\pi\)
0.521455 + 0.853279i \(0.325389\pi\)
\(114\) −1.08834 3.02869i −0.101932 0.283662i
\(115\) 2.13186 3.69249i 0.198797 0.344326i
\(116\) −0.171809 1.05288i −0.0159521 0.0977576i
\(117\) −9.88603 + 5.76843i −0.913964 + 0.533291i
\(118\) −11.0632 9.40421i −1.01845 0.865728i
\(119\) −4.76887 + 8.25993i −0.437162 + 0.757187i
\(120\) −0.0826465 + 4.89828i −0.00754456 + 0.447150i
\(121\) −0.624807 1.08220i −0.0568006 0.0983816i
\(122\) −3.14725 + 17.2054i −0.284939 + 1.55770i
\(123\) 17.2587 10.0173i 1.55616 0.903225i
\(124\) −0.337726 + 0.892252i −0.0303287 + 0.0801266i
\(125\) −1.00000 −0.0894427
\(126\) 2.06625 11.5965i 0.184076 1.03310i
\(127\) 0.554852i 0.0492352i −0.999697 0.0246176i \(-0.992163\pi\)
0.999697 0.0246176i \(-0.00783681\pi\)
\(128\) −7.65254 + 8.33298i −0.676395 + 0.736539i
\(129\) 10.7974 18.8012i 0.950654 1.65535i
\(130\) 0.970876 5.30758i 0.0851514 0.465505i
\(131\) 5.21744 3.01229i 0.455850 0.263185i −0.254448 0.967087i \(-0.581894\pi\)
0.710298 + 0.703901i \(0.248560\pi\)
\(132\) −10.6716 + 1.76657i −0.928847 + 0.153760i
\(133\) −3.15906 1.82389i −0.273926 0.158151i
\(134\) −6.37400 + 7.49841i −0.550629 + 0.647764i
\(135\) −2.62903 4.48199i −0.226271 0.385748i
\(136\) −5.01868 + 8.32013i −0.430348 + 0.713445i
\(137\) 7.48963 + 4.32414i 0.639883 + 0.369436i 0.784569 0.620041i \(-0.212884\pi\)
−0.144687 + 0.989478i \(0.546217\pi\)
\(138\) −6.74592 + 7.97298i −0.574251 + 0.678705i
\(139\) 4.72886 + 8.19062i 0.401096 + 0.694719i 0.993859 0.110658i \(-0.0352959\pi\)
−0.592762 + 0.805378i \(0.701963\pi\)
\(140\) 3.51459 + 4.29891i 0.297037 + 0.363324i
\(141\) −2.63448 + 4.58735i −0.221863 + 0.386325i
\(142\) 3.74713 + 10.5035i 0.314452 + 0.881434i
\(143\) 11.9135 0.996257
\(144\) 2.33104 11.7714i 0.194253 0.980951i
\(145\) −0.533403 −0.0442967
\(146\) 3.76615 + 10.5568i 0.311689 + 0.873687i
\(147\) −0.615801 1.06096i −0.0507904 0.0875067i
\(148\) 2.86414 + 3.50331i 0.235431 + 0.287970i
\(149\) −5.42917 9.40360i −0.444775 0.770373i 0.553261 0.833008i \(-0.313383\pi\)
−0.998037 + 0.0626346i \(0.980050\pi\)
\(150\) 2.41052 + 0.435217i 0.196818 + 0.0355353i
\(151\) −9.37631 5.41342i −0.763033 0.440538i 0.0673504 0.997729i \(-0.478545\pi\)
−0.830384 + 0.557192i \(0.811879\pi\)
\(152\) −3.18209 1.91943i −0.258101 0.155686i
\(153\) −0.0473521 10.3059i −0.00382819 0.833180i
\(154\) −7.94067 + 9.34145i −0.639877 + 0.752755i
\(155\) 0.413107 + 0.238507i 0.0331815 + 0.0191574i
\(156\) −4.65026 + 12.3715i −0.372319 + 0.990509i
\(157\) 14.2718 8.23981i 1.13901 0.657608i 0.192826 0.981233i \(-0.438235\pi\)
0.946186 + 0.323625i \(0.104902\pi\)
\(158\) −0.0550079 + 0.300717i −0.00437620 + 0.0239238i
\(159\) 24.7417 0.0568397i 1.96214 0.00450768i
\(160\) 3.49588 + 4.44734i 0.276374 + 0.351593i
\(161\) 11.8377i 0.932940i
\(162\) 4.38668 + 11.9481i 0.344650 + 0.938731i
\(163\) 7.55915 0.592078 0.296039 0.955176i \(-0.404334\pi\)
0.296039 + 0.955176i \(0.404334\pi\)
\(164\) 8.15695 21.5501i 0.636951 1.68278i
\(165\) 0.0124249 + 5.40842i 0.000967276 + 0.421045i
\(166\) 2.31081 12.6327i 0.179353 0.980488i
\(167\) 10.6372 + 18.4242i 0.823131 + 1.42570i 0.903340 + 0.428926i \(0.141108\pi\)
−0.0802091 + 0.996778i \(0.525559\pi\)
\(168\) −6.60101 11.8922i −0.509279 0.917504i
\(169\) 0.778243 1.34796i 0.0598649 0.103689i
\(170\) 3.70163 + 3.14656i 0.283902 + 0.241330i
\(171\) 3.94155 0.0181101i 0.301418 0.00138491i
\(172\) −4.03189 24.7083i −0.307429 1.88399i
\(173\) 10.3166 17.8689i 0.784356 1.35854i −0.145027 0.989428i \(-0.546327\pi\)
0.929383 0.369116i \(-0.120340\pi\)
\(174\) 1.28578 + 0.232146i 0.0974745 + 0.0175990i
\(175\) 2.40441 1.38819i 0.181756 0.104937i
\(176\) −8.27046 + 9.35979i −0.623410 + 0.705521i
\(177\) 15.3804 8.92706i 1.15606 0.670999i
\(178\) 6.42305 2.29143i 0.481428 0.171750i
\(179\) 7.50778i 0.561158i −0.959831 0.280579i \(-0.909474\pi\)
0.959831 0.280579i \(-0.0905264\pi\)
\(180\) −5.62117 2.09820i −0.418977 0.156390i
\(181\) 15.2146i 1.13089i 0.824785 + 0.565447i \(0.191296\pi\)
−0.824785 + 0.565447i \(0.808704\pi\)
\(182\) 5.03352 + 14.1093i 0.373110 + 1.04585i
\(183\) −18.5764 10.6683i −1.37321 0.788621i
\(184\) −0.231148 + 12.0574i −0.0170404 + 0.888884i
\(185\) 1.95942 1.13127i 0.144060 0.0831728i
\(186\) −0.891998 0.754717i −0.0654045 0.0553385i
\(187\) −5.36351 + 9.28987i −0.392219 + 0.679342i
\(188\) 0.983753 + 6.02865i 0.0717476 + 0.439684i
\(189\) 12.5431 + 7.12695i 0.912376 + 0.518410i
\(190\) −1.20342 + 1.41571i −0.0873054 + 0.102707i
\(191\) 6.80108 11.7798i 0.492109 0.852358i −0.507850 0.861446i \(-0.669559\pi\)
0.999959 + 0.00908769i \(0.00289274\pi\)
\(192\) −6.49133 12.2418i −0.468471 0.883479i
\(193\) −11.0958 19.2185i −0.798696 1.38338i −0.920466 0.390823i \(-0.872190\pi\)
0.121770 0.992558i \(-0.461143\pi\)
\(194\) −11.6890 2.13818i −0.839221 0.153512i
\(195\) 5.73052 + 3.29099i 0.410371 + 0.235673i
\(196\) −1.32477 0.501441i −0.0946267 0.0358172i
\(197\) −5.87131 −0.418314 −0.209157 0.977882i \(-0.567072\pi\)
−0.209157 + 0.977882i \(0.567072\pi\)
\(198\) 2.32389 13.0425i 0.165151 0.926889i
\(199\) 17.4689i 1.23834i 0.785259 + 0.619168i \(0.212530\pi\)
−0.785259 + 0.619168i \(0.787470\pi\)
\(200\) 2.47615 1.36700i 0.175090 0.0966618i
\(201\) −6.05059 10.4246i −0.426776 0.735291i
\(202\) 3.09021 + 0.565269i 0.217427 + 0.0397722i
\(203\) 1.28252 0.740464i 0.0900153 0.0519704i
\(204\) −7.55341 9.19585i −0.528844 0.643838i
\(205\) −9.97758 5.76056i −0.696864 0.402335i
\(206\) −15.9176 13.5307i −1.10903 0.942729i
\(207\) −6.44641 11.0480i −0.448056 0.767887i
\(208\) 4.85145 + 14.4695i 0.336388 + 1.00328i
\(209\) −3.55297 2.05131i −0.245764 0.141892i
\(210\) −6.40003 + 2.29981i −0.441644 + 0.158702i
\(211\) −8.80440 15.2497i −0.606120 1.04983i −0.991873 0.127228i \(-0.959392\pi\)
0.385754 0.922602i \(-0.373941\pi\)
\(212\) 22.1183 18.0829i 1.51909 1.24194i
\(213\) −13.6582 + 0.0313772i −0.935842 + 0.00214993i
\(214\) 18.7485 6.68854i 1.28162 0.457219i
\(215\) −12.5176 −0.853690
\(216\) 12.6368 + 7.50416i 0.859822 + 0.510594i
\(217\) −1.32437 −0.0899042
\(218\) 21.9876 7.84408i 1.48919 0.531268i
\(219\) −13.7275 + 0.0315365i −0.927617 + 0.00213104i
\(220\) 3.95283 + 4.83495i 0.266499 + 0.325972i
\(221\) 6.55339 + 11.3508i 0.440829 + 0.763538i
\(222\) −5.21557 + 1.87418i −0.350046 + 0.125787i
\(223\) 7.41753 + 4.28251i 0.496714 + 0.286778i 0.727356 0.686261i \(-0.240749\pi\)
−0.230641 + 0.973039i \(0.574082\pi\)
\(224\) −14.5793 5.84028i −0.974119 0.390220i
\(225\) −1.48805 + 2.60494i −0.0992031 + 0.173663i
\(226\) 0.571664 + 0.485941i 0.0380265 + 0.0323243i
\(227\) 20.0247 + 11.5612i 1.32908 + 0.767347i 0.985158 0.171651i \(-0.0549100\pi\)
0.343925 + 0.938997i \(0.388243\pi\)
\(228\) 3.51701 2.88885i 0.232920 0.191319i
\(229\) −6.36677 + 3.67586i −0.420728 + 0.242907i −0.695389 0.718634i \(-0.744768\pi\)
0.274661 + 0.961541i \(0.411434\pi\)
\(230\) 5.93139 + 1.08499i 0.391104 + 0.0715418i
\(231\) −7.53777 12.9868i −0.495949 0.854469i
\(232\) 1.32078 0.729165i 0.0867138 0.0478720i
\(233\) 20.6717i 1.35425i 0.735868 + 0.677125i \(0.236774\pi\)
−0.735868 + 0.677125i \(0.763226\pi\)
\(234\) −12.3812 10.4270i −0.809385 0.681634i
\(235\) 3.05419 0.199233
\(236\) 7.26922 19.2048i 0.473186 1.25013i
\(237\) −0.324680 0.186461i −0.0210902 0.0121119i
\(238\) −13.2683 2.42706i −0.860053 0.157323i
\(239\) −2.31092 4.00263i −0.149481 0.258908i 0.781555 0.623837i \(-0.214427\pi\)
−0.931036 + 0.364928i \(0.881094\pi\)
\(240\) −6.56373 + 2.21752i −0.423687 + 0.143141i
\(241\) −10.0859 + 17.4693i −0.649690 + 1.12530i 0.333507 + 0.942748i \(0.391768\pi\)
−0.983197 + 0.182548i \(0.941565\pi\)
\(242\) 1.14457 1.34648i 0.0735760 0.0865553i
\(243\) −15.5874 + 0.179054i −0.999934 + 0.0114863i
\(244\) −24.4129 + 3.98369i −1.56288 + 0.255030i
\(245\) −0.354125 + 0.613362i −0.0226242 + 0.0391863i
\(246\) 21.5440 + 18.2283i 1.37360 + 1.16220i
\(247\) −4.34119 + 2.50639i −0.276223 + 0.159478i
\(248\) −1.34895 0.0258603i −0.0856586 0.00164213i
\(249\) 13.6394 + 7.83296i 0.864359 + 0.496394i
\(250\) −0.475189 1.33199i −0.0300536 0.0842424i
\(251\) 15.2472i 0.962397i −0.876612 0.481199i \(-0.840202\pi\)
0.876612 0.481199i \(-0.159798\pi\)
\(252\) 16.4283 2.75831i 1.03488 0.173757i
\(253\) 13.3137i 0.837027i
\(254\) 0.739057 0.263659i 0.0463726 0.0165435i
\(255\) −5.14614 + 2.98691i −0.322264 + 0.187048i
\(256\) −14.7358 6.23336i −0.920990 0.389585i
\(257\) 1.24545 0.719060i 0.0776889 0.0448537i −0.460652 0.887581i \(-0.652384\pi\)
0.538341 + 0.842727i \(0.319051\pi\)
\(258\) 30.1738 + 5.44785i 1.87854 + 0.339168i
\(259\) −3.14084 + 5.44009i −0.195162 + 0.338031i
\(260\) 7.53099 1.22890i 0.467052 0.0762134i
\(261\) −0.793729 + 1.38948i −0.0491306 + 0.0860069i
\(262\) 6.49161 + 5.51817i 0.401053 + 0.340914i
\(263\) −2.20868 + 3.82555i −0.136193 + 0.235893i −0.926053 0.377395i \(-0.876820\pi\)
0.789860 + 0.613288i \(0.210153\pi\)
\(264\) −7.42410 13.3751i −0.456922 0.823178i
\(265\) −7.14233 12.3709i −0.438750 0.759937i
\(266\) 0.928246 5.07453i 0.0569144 0.311139i
\(267\) 0.0191877 + 8.35219i 0.00117427 + 0.511145i
\(268\) −13.0167 4.92694i −0.795119 0.300961i
\(269\) −24.9314 −1.52010 −0.760048 0.649867i \(-0.774825\pi\)
−0.760048 + 0.649867i \(0.774825\pi\)
\(270\) 4.72068 5.63163i 0.287291 0.342730i
\(271\) 21.5066i 1.30643i 0.757172 + 0.653215i \(0.226580\pi\)
−0.757172 + 0.653215i \(0.773420\pi\)
\(272\) −13.4671 2.73120i −0.816566 0.165603i
\(273\) −18.3470 + 0.0421491i −1.11041 + 0.00255098i
\(274\) −2.20072 + 12.0309i −0.132951 + 0.726813i
\(275\) 2.70422 1.56128i 0.163070 0.0941488i
\(276\) −13.8255 5.19682i −0.832198 0.312812i
\(277\) −0.693110 0.400167i −0.0416449 0.0240437i 0.479033 0.877797i \(-0.340987\pi\)
−0.520678 + 0.853753i \(0.674321\pi\)
\(278\) −8.66272 + 10.1909i −0.519556 + 0.611208i
\(279\) 1.23602 0.721209i 0.0739986 0.0431776i
\(280\) −4.05601 + 6.72419i −0.242393 + 0.401847i
\(281\) −17.8052 10.2798i −1.06217 0.613244i −0.136139 0.990690i \(-0.543469\pi\)
−0.926032 + 0.377445i \(0.876803\pi\)
\(282\) −7.36218 1.32924i −0.438411 0.0791549i
\(283\) 7.32132 + 12.6809i 0.435207 + 0.753801i 0.997313 0.0732645i \(-0.0233417\pi\)
−0.562105 + 0.827066i \(0.690008\pi\)
\(284\) −12.2099 + 9.98228i −0.724527 + 0.592339i
\(285\) −1.14236 1.96817i −0.0676677 0.116585i
\(286\) 5.66116 + 15.8686i 0.334751 + 0.938333i
\(287\) 31.9869 1.88813
\(288\) 16.7871 2.48873i 0.989188 0.146650i
\(289\) 5.19853 0.305796
\(290\) −0.253467 0.710488i −0.0148841 0.0417213i
\(291\) 7.24781 12.6204i 0.424874 0.739824i
\(292\) −12.2719 + 10.0329i −0.718159 + 0.587133i
\(293\) −13.4417 23.2817i −0.785273 1.36013i −0.928836 0.370491i \(-0.879189\pi\)
0.143563 0.989641i \(-0.454144\pi\)
\(294\) 1.12057 1.32440i 0.0653529 0.0772404i
\(295\) −8.89170 5.13363i −0.517695 0.298891i
\(296\) −3.30536 + 5.47974i −0.192120 + 0.318503i
\(297\) 14.1071 + 8.01562i 0.818577 + 0.465113i
\(298\) 9.94562 11.7001i 0.576134 0.677768i
\(299\) 14.0879 + 8.13368i 0.814727 + 0.470383i
\(300\) 0.565745 + 3.41759i 0.0326633 + 0.197315i
\(301\) 30.0973 17.3767i 1.73478 1.00158i
\(302\) 2.75510 15.0615i 0.158538 0.866694i
\(303\) −1.91610 + 3.33646i −0.110077 + 0.191675i
\(304\) 1.04456 5.15060i 0.0599098 0.295407i
\(305\) 12.3679i 0.708184i
\(306\) 13.7048 4.96030i 0.783452 0.283562i
\(307\) −21.3839 −1.22044 −0.610221 0.792231i \(-0.708920\pi\)
−0.610221 + 0.792231i \(0.708920\pi\)
\(308\) −16.2160 6.13793i −0.923994 0.349741i
\(309\) 22.1292 12.8442i 1.25889 0.730680i
\(310\) −0.121386 + 0.663590i −0.00689424 + 0.0376894i
\(311\) −10.7043 18.5404i −0.606985 1.05133i −0.991734 0.128308i \(-0.959045\pi\)
0.384749 0.923021i \(-0.374288\pi\)
\(312\) −18.6884 0.315321i −1.05802 0.0178515i
\(313\) 2.91819 5.05445i 0.164946 0.285694i −0.771690 0.635998i \(-0.780588\pi\)
0.936636 + 0.350304i \(0.113922\pi\)
\(314\) 17.7571 + 15.0944i 1.00209 + 0.851825i
\(315\) −0.0382692 8.32903i −0.00215622 0.469288i
\(316\) −0.426691 + 0.0696273i −0.0240032 + 0.00391684i
\(317\) 4.19064 7.25841i 0.235370 0.407673i −0.724010 0.689789i \(-0.757703\pi\)
0.959380 + 0.282117i \(0.0910365\pi\)
\(318\) 11.8327 + 32.9287i 0.663544 + 1.84655i
\(319\) 1.44244 0.832792i 0.0807611 0.0466274i
\(320\) −4.26260 + 6.76980i −0.238287 + 0.378444i
\(321\) 0.0560076 + 24.3795i 0.00312604 + 1.36073i
\(322\) −15.7677 + 5.62513i −0.878697 + 0.313476i
\(323\) 4.51355i 0.251140i
\(324\) −13.8302 + 11.5206i −0.768347 + 0.640034i
\(325\) 3.81530i 0.211635i
\(326\) 3.59202 + 10.0687i 0.198944 + 0.557654i
\(327\) 0.0656837 + 28.5914i 0.00363232 + 1.58111i
\(328\) 32.5806 + 0.624591i 1.79896 + 0.0344873i
\(329\) −7.34353 + 4.23979i −0.404862 + 0.233747i
\(330\) −7.19805 + 2.58657i −0.396240 + 0.142386i
\(331\) −0.901119 + 1.56078i −0.0495300 + 0.0857884i −0.889727 0.456492i \(-0.849106\pi\)
0.840197 + 0.542281i \(0.182439\pi\)
\(332\) 17.9247 2.92495i 0.983745 0.160527i
\(333\) −0.0311866 6.78757i −0.00170902 0.371956i
\(334\) −19.4861 + 22.9236i −1.06623 + 1.25432i
\(335\) −3.47947 + 6.02663i −0.190104 + 0.329270i
\(336\) 12.7036 14.4435i 0.693036 0.787959i
\(337\) −11.9797 20.7495i −0.652577 1.13030i −0.982495 0.186287i \(-0.940355\pi\)
0.329918 0.944009i \(-0.392979\pi\)
\(338\) 2.16528 + 0.396078i 0.117776 + 0.0215438i
\(339\) −0.794748 + 0.461286i −0.0431648 + 0.0250536i
\(340\) −2.43221 + 6.42575i −0.131905 + 0.348485i
\(341\) −1.48951 −0.0806614
\(342\) 1.89710 + 5.24149i 0.102583 + 0.283427i
\(343\) 17.4682i 0.943197i
\(344\) 30.9953 17.1115i 1.67115 0.922593i
\(345\) −3.67779 + 6.40405i −0.198005 + 0.344782i
\(346\) 28.7035 + 5.25051i 1.54311 + 0.282269i
\(347\) −15.0256 + 8.67502i −0.806615 + 0.465699i −0.845779 0.533533i \(-0.820864\pi\)
0.0391641 + 0.999233i \(0.487530\pi\)
\(348\) 0.301770 + 1.82296i 0.0161766 + 0.0977206i
\(349\) −7.29528 4.21193i −0.390507 0.225460i 0.291873 0.956457i \(-0.405722\pi\)
−0.682380 + 0.730998i \(0.739055\pi\)
\(350\) 2.99160 + 2.54300i 0.159908 + 0.135929i
\(351\) 17.1001 10.0305i 0.912736 0.535390i
\(352\) −16.3972 6.56850i −0.873972 0.350102i
\(353\) 14.9442 + 8.62801i 0.795397 + 0.459223i 0.841859 0.539697i \(-0.181461\pi\)
−0.0464619 + 0.998920i \(0.514795\pi\)
\(354\) 19.1993 + 16.2445i 1.02043 + 0.863386i
\(355\) 3.94278 + 6.82910i 0.209261 + 0.362451i
\(356\) 6.10432 + 7.46657i 0.323528 + 0.395728i
\(357\) 8.22704 14.3256i 0.435421 0.758189i
\(358\) 10.0003 3.56761i 0.528531 0.188554i
\(359\) −7.13071 −0.376344 −0.188172 0.982136i \(-0.560256\pi\)
−0.188172 + 0.982136i \(0.560256\pi\)
\(360\) 0.123657 8.48438i 0.00651729 0.447166i
\(361\) −17.2738 −0.909146
\(362\) −20.2657 + 7.22982i −1.06514 + 0.379991i
\(363\) 1.08650 + 1.87193i 0.0570265 + 0.0982508i
\(364\) −16.4016 + 13.4092i −0.859679 + 0.702833i
\(365\) 3.96279 + 6.86376i 0.207422 + 0.359266i
\(366\) 5.38272 29.8130i 0.281359 1.55835i
\(367\) 29.3780 + 16.9614i 1.53352 + 0.885379i 0.999196 + 0.0401004i \(0.0127678\pi\)
0.534326 + 0.845279i \(0.320566\pi\)
\(368\) −16.1702 + 5.42166i −0.842929 + 0.282623i
\(369\) −29.8530 + 17.4190i −1.55409 + 0.906798i
\(370\) 2.43794 + 2.07236i 0.126742 + 0.107737i
\(371\) 34.3462 + 19.8298i 1.78317 + 1.02951i
\(372\) 0.581408 1.54676i 0.0301446 0.0801960i
\(373\) −8.48032 + 4.89612i −0.439095 + 0.253511i −0.703213 0.710979i \(-0.748252\pi\)
0.264119 + 0.964490i \(0.414919\pi\)
\(374\) −14.9227 2.72970i −0.771634 0.141149i
\(375\) 1.73205 0.00397907i 0.0894425 0.000205478i
\(376\) −7.56262 + 4.17509i −0.390013 + 0.215314i
\(377\) 2.03509i 0.104813i
\(378\) −3.53269 + 20.0939i −0.181702 + 1.03352i
\(379\) 15.9453 0.819054 0.409527 0.912298i \(-0.365694\pi\)
0.409527 + 0.912298i \(0.365694\pi\)
\(380\) −2.45757 0.930215i −0.126071 0.0477190i
\(381\) 0.00220780 + 0.961030i 0.000113109 + 0.0492350i
\(382\) 18.9224 + 3.46133i 0.968154 + 0.177097i
\(383\) 3.70162 + 6.41139i 0.189144 + 0.327607i 0.944965 0.327171i \(-0.106095\pi\)
−0.755821 + 0.654778i \(0.772762\pi\)
\(384\) 13.2214 14.4636i 0.674702 0.738091i
\(385\) −4.33470 + 7.50792i −0.220917 + 0.382639i
\(386\) 20.3263 23.9120i 1.03458 1.21709i
\(387\) −18.6267 + 32.6075i −0.946849 + 1.65753i
\(388\) −2.70644 16.5856i −0.137399 0.842009i
\(389\) −13.0021 + 22.5203i −0.659233 + 1.14182i 0.321582 + 0.946882i \(0.395786\pi\)
−0.980815 + 0.194943i \(0.937548\pi\)
\(390\) −1.66048 + 9.19683i −0.0840818 + 0.465700i
\(391\) −12.6849 + 7.32363i −0.641503 + 0.370372i
\(392\) 0.0383961 2.00286i 0.00193930 0.101160i
\(393\) −9.02487 + 5.23819i −0.455244 + 0.264232i
\(394\) −2.78998 7.82053i −0.140557 0.393993i
\(395\) 0.216167i 0.0108766i
\(396\) 18.4767 3.10225i 0.928491 0.155894i
\(397\) 26.9039i 1.35027i −0.737694 0.675135i \(-0.764085\pi\)
0.737694 0.675135i \(-0.235915\pi\)
\(398\) −23.2684 + 8.30101i −1.16634 + 0.416092i
\(399\) 5.47890 + 3.14649i 0.274288 + 0.157521i
\(400\) 2.99747 + 2.64862i 0.149874 + 0.132431i
\(401\) −9.03940 + 5.21890i −0.451406 + 0.260619i −0.708424 0.705787i \(-0.750593\pi\)
0.257018 + 0.966407i \(0.417260\pi\)
\(402\) 11.0102 13.0130i 0.549140 0.649027i
\(403\) −0.909976 + 1.57613i −0.0453291 + 0.0785124i
\(404\) 0.715500 + 4.38474i 0.0355975 + 0.218149i
\(405\) 4.57143 + 7.75255i 0.227156 + 0.385227i
\(406\) 1.59573 + 1.35644i 0.0791947 + 0.0673192i
\(407\) −3.53247 + 6.11842i −0.175098 + 0.303279i
\(408\) 8.65948 14.4308i 0.428708 0.714432i
\(409\) 2.09390 + 3.62675i 0.103537 + 0.179331i 0.913140 0.407647i \(-0.133651\pi\)
−0.809603 + 0.586978i \(0.800317\pi\)
\(410\) 2.93177 16.0274i 0.144790 0.791536i
\(411\) −12.9896 7.45981i −0.640730 0.367965i
\(412\) 10.4589 27.6317i 0.515273 1.36132i
\(413\) 28.5057 1.40268
\(414\) 11.6525 13.8364i 0.572690 0.680023i
\(415\) 9.08089i 0.445763i
\(416\) −16.9679 + 13.3378i −0.831920 + 0.653941i
\(417\) −8.22319 14.1677i −0.402691 0.693796i
\(418\) 1.04399 5.70728i 0.0510632 0.279152i
\(419\) 2.80884 1.62169i 0.137221 0.0792245i −0.429818 0.902916i \(-0.641422\pi\)
0.567039 + 0.823691i \(0.308089\pi\)
\(420\) −6.10454 7.43193i −0.297871 0.362641i
\(421\) 5.45534 + 3.14964i 0.265877 + 0.153504i 0.627013 0.779009i \(-0.284277\pi\)
−0.361135 + 0.932513i \(0.617611\pi\)
\(422\) 16.1286 18.9738i 0.785130 0.923632i
\(423\) 4.54478 7.95599i 0.220975 0.386833i
\(424\) 34.5965 + 20.8685i 1.68016 + 1.01346i
\(425\) 2.97508 + 1.71766i 0.144313 + 0.0833189i
\(426\) −6.53200 18.1776i −0.316477 0.880709i
\(427\) −17.1690 29.7375i −0.830864 1.43910i
\(428\) 17.8181 + 21.7945i 0.861272 + 1.05347i
\(429\) −20.6347 + 0.0474046i −0.996254 + 0.00228872i
\(430\) −5.94820 16.6732i −0.286848 0.804055i
\(431\) 16.9856 0.818167 0.409084 0.912497i \(-0.365848\pi\)
0.409084 + 0.912497i \(0.365848\pi\)
\(432\) −3.99062 + 20.3979i −0.191999 + 0.981395i
\(433\) −17.6526 −0.848331 −0.424166 0.905585i \(-0.639433\pi\)
−0.424166 + 0.905585i \(0.639433\pi\)
\(434\) −0.629326 1.76405i −0.0302086 0.0846770i
\(435\) 0.923879 0.00212245i 0.0442966 0.000101764i
\(436\) 20.8965 + 25.5598i 1.00076 + 1.22409i
\(437\) −2.80097 4.85142i −0.133989 0.232075i
\(438\) −6.56515 18.2699i −0.313695 0.872968i
\(439\) −33.1600 19.1449i −1.58264 0.913738i −0.994472 0.105000i \(-0.966516\pi\)
−0.588168 0.808738i \(-0.700151\pi\)
\(440\) −4.56176 + 7.56263i −0.217473 + 0.360534i
\(441\) 1.07082 + 1.83519i 0.0509913 + 0.0873898i
\(442\) −12.0051 + 14.1228i −0.571023 + 0.671754i
\(443\) −11.3515 6.55380i −0.539327 0.311381i 0.205479 0.978661i \(-0.434125\pi\)
−0.744806 + 0.667281i \(0.767458\pi\)
\(444\) −4.97476 6.05649i −0.236092 0.287428i
\(445\) 4.17610 2.41107i 0.197966 0.114296i
\(446\) −2.17953 + 11.9151i −0.103204 + 0.564195i
\(447\) 9.44099 + 16.2659i 0.446544 + 0.769349i
\(448\) 0.851284 22.1947i 0.0402194 1.04860i
\(449\) 24.9459i 1.17727i 0.808400 + 0.588634i \(0.200334\pi\)
−0.808400 + 0.588634i \(0.799666\pi\)
\(450\) −4.17686 0.744225i −0.196899 0.0350831i
\(451\) 35.9754 1.69401
\(452\) −0.375620 + 0.992365i −0.0176677 + 0.0466769i
\(453\) 16.2617 + 9.33898i 0.764043 + 0.438783i
\(454\) −5.88396 + 32.1664i −0.276148 + 1.50964i
\(455\) 5.29634 + 9.17354i 0.248296 + 0.430062i
\(456\) 5.51916 + 3.31187i 0.258458 + 0.155093i
\(457\) 13.2777 22.9976i 0.621103 1.07578i −0.368178 0.929755i \(-0.620018\pi\)
0.989281 0.146026i \(-0.0466483\pi\)
\(458\) −7.92162 6.73375i −0.370153 0.314647i
\(459\) 0.123024 + 17.8501i 0.00574226 + 0.833169i
\(460\) 1.37334 + 8.41612i 0.0640324 + 0.392404i
\(461\) −5.99710 + 10.3873i −0.279313 + 0.483784i −0.971214 0.238208i \(-0.923440\pi\)
0.691901 + 0.721992i \(0.256773\pi\)
\(462\) 13.7164 16.2114i 0.638146 0.754223i
\(463\) 21.9062 12.6476i 1.01807 0.587782i 0.104525 0.994522i \(-0.466668\pi\)
0.913544 + 0.406740i \(0.133334\pi\)
\(464\) 1.59886 + 1.41278i 0.0742253 + 0.0655867i
\(465\) −0.716469 0.411462i −0.0332255 0.0190811i
\(466\) −27.5345 + 9.82297i −1.27551 + 0.455040i
\(467\) 7.44030i 0.344296i 0.985071 + 0.172148i \(0.0550707\pi\)
−0.985071 + 0.172148i \(0.944929\pi\)
\(468\) 8.00524 21.4464i 0.370042 0.991362i
\(469\) 19.3206i 0.892144i
\(470\) 1.45132 + 4.06815i 0.0669443 + 0.187650i
\(471\) −24.6866 + 14.3285i −1.13750 + 0.660223i
\(472\) 29.0348 + 0.556616i 1.33644 + 0.0256203i
\(473\) 33.8502 19.5434i 1.55643 0.898607i
\(474\) 0.0940797 0.521075i 0.00432122 0.0239337i
\(475\) −0.656931 + 1.13784i −0.0301421 + 0.0522076i
\(476\) −3.07210 18.8265i −0.140810 0.862911i
\(477\) −42.8535 + 0.196898i −1.96213 + 0.00901534i
\(478\) 4.23333 4.98012i 0.193628 0.227785i
\(479\) −19.5734 + 33.9022i −0.894333 + 1.54903i −0.0597054 + 0.998216i \(0.519016\pi\)
−0.834628 + 0.550814i \(0.814317\pi\)
\(480\) −6.07273 7.68908i −0.277181 0.350957i
\(481\) 4.31614 + 7.47578i 0.196799 + 0.340866i
\(482\) −28.0616 5.13310i −1.27817 0.233806i
\(483\) −0.0471030 20.5034i −0.00214326 0.932937i
\(484\) 2.33739 + 0.884727i 0.106245 + 0.0402149i
\(485\) −8.40251 −0.381538
\(486\) −7.64547 20.6772i −0.346805 0.937937i
\(487\) 20.0755i 0.909707i −0.890566 0.454854i \(-0.849692\pi\)
0.890566 0.454854i \(-0.150308\pi\)
\(488\) −16.9070 30.6247i −0.765343 1.38632i
\(489\) −13.0928 + 0.0300784i −0.592077 + 0.00136019i
\(490\) −0.985268 0.180228i −0.0445099 0.00814186i
\(491\) 18.3558 10.5977i 0.828385 0.478268i −0.0249145 0.999690i \(-0.507931\pi\)
0.853299 + 0.521421i \(0.174598\pi\)
\(492\) −14.0425 + 37.3583i −0.633083 + 1.68424i
\(493\) 1.58692 + 0.916207i 0.0714712 + 0.0412639i
\(494\) −5.40137 4.59141i −0.243019 0.206577i
\(495\) −0.0430410 9.36758i −0.00193455 0.421042i
\(496\) −0.606562 1.80908i −0.0272354 0.0812301i
\(497\) −18.9601 10.9466i −0.850479 0.491024i
\(498\) −3.95216 + 21.8896i −0.177100 + 0.980897i
\(499\) −4.07075 7.05075i −0.182232 0.315635i 0.760408 0.649445i \(-0.224999\pi\)
−0.942640 + 0.333810i \(0.891665\pi\)
\(500\) 1.54839 1.26589i 0.0692462 0.0566124i
\(501\) −18.4974 31.8692i −0.826404 1.42381i
\(502\) 20.3092 7.24532i 0.906442 0.323374i
\(503\) 9.59614 0.427871 0.213935 0.976848i \(-0.431372\pi\)
0.213935 + 0.976848i \(0.431372\pi\)
\(504\) 11.4806 + 20.5716i 0.511386 + 0.916331i
\(505\) 2.22137 0.0988495
\(506\) −17.7337 + 6.32653i −0.788361 + 0.281249i
\(507\) −1.34259 + 2.33782i −0.0596265 + 0.103826i
\(508\) 0.702383 + 0.859129i 0.0311632 + 0.0381177i
\(509\) −0.164517 0.284953i −0.00729211 0.0126303i 0.862356 0.506302i \(-0.168988\pi\)
−0.869648 + 0.493672i \(0.835655\pi\)
\(510\) −6.42392 5.43526i −0.284456 0.240677i
\(511\) −19.0564 11.0022i −0.843004 0.486708i
\(512\) 1.30047 22.5900i 0.0574731 0.998347i
\(513\) −6.82687 + 0.0470512i −0.301414 + 0.00207736i
\(514\) 1.54960 + 1.31723i 0.0683500 + 0.0581007i
\(515\) −12.7933 7.38623i −0.563741 0.325476i
\(516\) 7.08174 + 42.7799i 0.311756 + 1.88328i
\(517\) −8.25920 + 4.76845i −0.363239 + 0.209716i
\(518\) −8.73863 1.59849i −0.383953 0.0702337i
\(519\) −17.7977 + 30.9907i −0.781233 + 1.36034i
\(520\) 5.21553 + 9.44723i 0.228716 + 0.414289i
\(521\) 14.4490i 0.633021i −0.948589 0.316510i \(-0.897489\pi\)
0.948589 0.316510i \(-0.102511\pi\)
\(522\) −2.22795 0.396972i −0.0975147 0.0173750i
\(523\) 18.1246 0.792534 0.396267 0.918135i \(-0.370305\pi\)
0.396267 + 0.918135i \(0.370305\pi\)
\(524\) −4.26541 + 11.2689i −0.186335 + 0.492286i
\(525\) −4.15903 + 2.41397i −0.181515 + 0.105354i
\(526\) −6.14513 1.12408i −0.267940 0.0490123i
\(527\) −0.819351 1.41916i −0.0356915 0.0618194i
\(528\) 14.2876 16.2445i 0.621787 0.706951i
\(529\) 2.41035 4.17484i 0.104798 0.181515i
\(530\) 13.0839 15.3920i 0.568330 0.668586i
\(531\) −26.6041 + 15.5233i −1.15452 + 0.673653i
\(532\) 7.20031 1.17495i 0.312173 0.0509403i
\(533\) 21.9782 38.0674i 0.951983 1.64888i
\(534\) −11.1159 + 3.99442i −0.481032 + 0.172856i
\(535\) 12.1898 7.03777i 0.527010 0.304269i
\(536\) 0.377264 19.6793i 0.0162953 0.850015i
\(537\) 0.0298740 + 13.0038i 0.00128916 + 0.561156i
\(538\) −11.8471 33.2084i −0.510766 1.43172i
\(539\) 2.21155i 0.0952583i
\(540\) 9.74448 + 3.61180i 0.419336 + 0.155427i
\(541\) 3.63353i 0.156218i 0.996945 + 0.0781089i \(0.0248882\pi\)
−0.996945 + 0.0781089i \(0.975112\pi\)
\(542\) −28.6465 + 10.2197i −1.23047 + 0.438972i
\(543\) −0.0605401 26.3524i −0.00259802 1.13089i
\(544\) −2.76151 19.2359i −0.118399 0.824734i
\(545\) 14.2957 8.25365i 0.612363 0.353548i
\(546\) −8.77444 24.4180i −0.375511 1.04499i
\(547\) 11.7873 20.4162i 0.503987 0.872932i −0.496002 0.868321i \(-0.665199\pi\)
0.999989 0.00461043i \(-0.00146755\pi\)
\(548\) −17.0708 + 2.78561i −0.729228 + 0.118995i
\(549\) 32.2176 + 18.4040i 1.37502 + 0.785464i
\(550\) 3.36462 + 2.86009i 0.143468 + 0.121954i
\(551\) −0.350409 + 0.606927i −0.0149279 + 0.0258560i
\(552\) 0.352381 20.8849i 0.0149984 0.888920i
\(553\) −0.300081 0.519755i −0.0127607 0.0221022i
\(554\) 0.203660 1.11337i 0.00865270 0.0473026i
\(555\) −3.38931 + 1.96721i −0.143868 + 0.0835036i
\(556\) −17.6906 6.69606i −0.750247 0.283976i
\(557\) −32.3117 −1.36909 −0.684544 0.728971i \(-0.739999\pi\)
−0.684544 + 0.728971i \(0.739999\pi\)
\(558\) 1.54799 + 1.30366i 0.0655314 + 0.0551881i
\(559\) 47.7582i 2.01996i
\(560\) −10.8839 2.20731i −0.459930 0.0932758i
\(561\) 9.25288 16.1118i 0.390657 0.680242i
\(562\) 5.23181 28.6012i 0.220691 1.20647i
\(563\) −13.2429 + 7.64582i −0.558124 + 0.322233i −0.752392 0.658716i \(-0.771100\pi\)
0.194268 + 0.980948i \(0.437767\pi\)
\(564\) −1.72789 10.4380i −0.0727575 0.439518i
\(565\) 0.459459 + 0.265268i 0.0193296 + 0.0111599i
\(566\) −13.4118 + 15.7777i −0.563741 + 0.663188i
\(567\) −21.7536 12.2943i −0.913565 0.516312i
\(568\) −19.0983 11.5201i −0.801348 0.483371i
\(569\) −18.3848 10.6145i −0.770730 0.444981i 0.0624050 0.998051i \(-0.480123\pi\)
−0.833135 + 0.553070i \(0.813456\pi\)
\(570\) 2.07875 2.45687i 0.0870693 0.102907i
\(571\) −20.3971 35.3288i −0.853591 1.47846i −0.877946 0.478760i \(-0.841086\pi\)
0.0243545 0.999703i \(-0.492247\pi\)
\(572\) −18.4468 + 15.0812i −0.771298 + 0.630577i
\(573\) −11.7329 + 20.4303i −0.490150 + 0.853486i
\(574\) 15.1998 + 42.6062i 0.634428 + 1.77835i
\(575\) 4.26372 0.177809
\(576\) 11.2920 + 21.1776i 0.470500 + 0.882400i
\(577\) 29.2113 1.21608 0.608040 0.793906i \(-0.291956\pi\)
0.608040 + 0.793906i \(0.291956\pi\)
\(578\) 2.47028 + 6.92439i 0.102750 + 0.288017i
\(579\) 19.2950 + 33.2433i 0.801872 + 1.38154i
\(580\) 0.825917 0.675231i 0.0342944 0.0280375i
\(581\) 12.6060 + 21.8342i 0.522984 + 0.905834i
\(582\) 20.2544 + 3.65692i 0.839571 + 0.151584i
\(583\) 38.6288 + 22.3024i 1.59984 + 0.923670i
\(584\) −19.1952 11.5785i −0.794305 0.479122i
\(585\) −9.93862 5.67734i −0.410911 0.234729i
\(586\) 24.6237 28.9674i 1.01719 1.19663i
\(587\) −2.09726 1.21086i −0.0865634 0.0499774i 0.456093 0.889932i \(-0.349248\pi\)
−0.542657 + 0.839954i \(0.682582\pi\)
\(588\) 2.29656 + 0.863247i 0.0947087 + 0.0355997i
\(589\) 0.542766 0.313366i 0.0223643 0.0129120i
\(590\) 2.61270 14.2831i 0.107563 0.588026i
\(591\) 10.1694 0.0233624i 0.418313 0.000961000i
\(592\) −8.86962 1.79880i −0.364539 0.0739301i
\(593\) 7.77622i 0.319331i 0.987171 + 0.159666i \(0.0510416\pi\)
−0.987171 + 0.159666i \(0.948958\pi\)
\(594\) −3.97318 + 22.5994i −0.163022 + 0.927266i
\(595\) −9.53775 −0.391010
\(596\) 20.3104 + 7.68771i 0.831948 + 0.314901i
\(597\) −0.0695099 30.2569i −0.00284485 1.23833i
\(598\) −4.13954 + 22.6300i −0.169278 + 0.925410i
\(599\) −9.47635 16.4135i −0.387193 0.670638i 0.604878 0.796318i \(-0.293222\pi\)
−0.992071 + 0.125680i \(0.959889\pi\)
\(600\) −4.28336 + 2.37757i −0.174867 + 0.0970638i
\(601\) −11.5216 + 19.9560i −0.469976 + 0.814023i −0.999411 0.0343283i \(-0.989071\pi\)
0.529434 + 0.848351i \(0.322404\pi\)
\(602\) 37.4475 + 31.8321i 1.52625 + 1.29738i
\(603\) 10.5214 + 18.0317i 0.428464 + 0.734309i
\(604\) 21.3710 3.48731i 0.869574 0.141897i
\(605\) 0.624807 1.08220i 0.0254020 0.0439976i
\(606\) −5.35464 0.966777i −0.217517 0.0392726i
\(607\) −26.8628 + 15.5092i −1.09033 + 0.629500i −0.933663 0.358153i \(-0.883407\pi\)
−0.156662 + 0.987652i \(0.550073\pi\)
\(608\) 7.35690 1.05616i 0.298362 0.0428328i
\(609\) −2.21844 + 1.28762i −0.0898957 + 0.0521770i
\(610\) −16.4739 + 5.87708i −0.667009 + 0.237956i
\(611\) 11.6526i 0.471416i
\(612\) 13.1194 + 15.8976i 0.530322 + 0.642622i
\(613\) 43.8644i 1.77167i 0.464002 + 0.885834i \(0.346413\pi\)
−0.464002 + 0.885834i \(0.653587\pi\)
\(614\) −10.1614 28.4831i −0.410080 1.14948i
\(615\) 17.3045 + 9.93785i 0.697787 + 0.400733i
\(616\) 0.469991 24.5162i 0.0189365 0.987788i
\(617\) 20.2819 11.7098i 0.816520 0.471418i −0.0326947 0.999465i \(-0.510409\pi\)
0.849215 + 0.528047i \(0.177076\pi\)
\(618\) 27.6239 + 23.3725i 1.11120 + 0.940179i
\(619\) 13.1137 22.7136i 0.527084 0.912935i −0.472418 0.881374i \(-0.656619\pi\)
0.999502 0.0315610i \(-0.0100479\pi\)
\(620\) −0.941576 + 0.153646i −0.0378146 + 0.00617058i
\(621\) 11.2094 + 19.1099i 0.449819 + 0.766855i
\(622\) 19.6091 23.0682i 0.786251 0.924951i
\(623\) −6.69404 + 11.5944i −0.268191 + 0.464521i
\(624\) −8.46051 25.0426i −0.338691 1.00251i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 8.11916 + 1.48518i 0.324507 + 0.0593596i
\(627\) 6.16207 + 3.53882i 0.246089 + 0.141327i
\(628\) −11.6676 + 30.8250i −0.465587 + 1.23005i
\(629\) −7.77258 −0.309913
\(630\) 11.0760 4.00884i 0.441278 0.159716i
\(631\) 7.35292i 0.292715i 0.989232 + 0.146358i \(0.0467550\pi\)
−0.989232 + 0.146358i \(0.953245\pi\)
\(632\) −0.295502 0.535262i −0.0117544 0.0212916i
\(633\) 15.3103 + 26.3781i 0.608530 + 1.04843i
\(634\) 11.6595 + 2.13278i 0.463057 + 0.0847035i
\(635\) 0.480516 0.277426i 0.0190687 0.0110093i
\(636\) −38.2379 + 31.4083i −1.51623 + 1.24542i
\(637\) −2.34016 1.35109i −0.0927204 0.0535322i
\(638\) 1.79470 + 1.52558i 0.0710529 + 0.0603983i
\(639\) 23.6565 0.108694i 0.935835 0.00429985i
\(640\) −11.0428 2.46080i −0.436507 0.0972718i
\(641\) 4.75502 + 2.74531i 0.187812 + 0.108433i 0.590958 0.806702i \(-0.298750\pi\)
−0.403146 + 0.915136i \(0.632083\pi\)
\(642\) −32.4466 + 11.6595i −1.28057 + 0.460162i
\(643\) −10.2614 17.7733i −0.404670 0.700909i 0.589613 0.807686i \(-0.299280\pi\)
−0.994283 + 0.106777i \(0.965947\pi\)
\(644\) −14.9852 18.3294i −0.590501 0.722278i
\(645\) 21.6810 0.0498082i 0.853688 0.00196120i
\(646\) 6.01200 2.14479i 0.236539 0.0843855i
\(647\) −39.5969 −1.55672 −0.778358 0.627820i \(-0.783947\pi\)
−0.778358 + 0.627820i \(0.783947\pi\)
\(648\) −21.9173 12.9473i −0.860993 0.508617i
\(649\) 32.0601 1.25847
\(650\) 5.08193 1.81299i 0.199330 0.0711111i
\(651\) 2.29387 0.00526977i 0.0899039 0.000206538i
\(652\) −11.7045 + 9.56907i −0.458384 + 0.374754i
\(653\) 22.5179 + 39.0021i 0.881193 + 1.52627i 0.850016 + 0.526757i \(0.176592\pi\)
0.0311765 + 0.999514i \(0.490075\pi\)
\(654\) −38.0523 + 13.6738i −1.48796 + 0.534688i
\(655\) 5.21744 + 3.01229i 0.203862 + 0.117700i
\(656\) 14.6500 + 43.6939i 0.571986 + 1.70596i
\(657\) 23.7765 0.109245i 0.927610 0.00426206i
\(658\) −9.13691 7.76680i −0.356194 0.302781i
\(659\) −22.1927 12.8129i −0.864504 0.499121i 0.00101427 0.999999i \(-0.499677\pi\)
−0.865518 + 0.500878i \(0.833010\pi\)
\(660\) −6.86572 8.35862i −0.267248 0.325359i
\(661\) −9.96758 + 5.75478i −0.387694 + 0.223835i −0.681160 0.732134i \(-0.738524\pi\)
0.293467 + 0.955969i \(0.405191\pi\)
\(662\) −2.50715 0.458614i −0.0974431 0.0178245i
\(663\) −11.3959 19.6341i −0.442582 0.762523i
\(664\) 12.4136 + 22.4856i 0.481741 + 0.872610i
\(665\) 3.64777i 0.141455i
\(666\) 9.02615 3.26691i 0.349756 0.126590i
\(667\) 2.27428 0.0880606
\(668\) −39.7935 15.0623i −1.53966 0.582777i
\(669\) −12.8645 7.38799i −0.497372 0.285636i
\(670\) −9.68081 1.77084i −0.374002 0.0684135i
\(671\) −19.3098 33.4455i −0.745445 1.29115i
\(672\) 25.2752 + 10.0576i 0.975012 + 0.387981i
\(673\) 23.4948 40.6943i 0.905660 1.56865i 0.0856300 0.996327i \(-0.472710\pi\)
0.820029 0.572321i \(-0.193957\pi\)
\(674\) 21.9455 25.8168i 0.845308 0.994425i
\(675\) 2.56700 4.51780i 0.0988039 0.173890i
\(676\) 0.501343 + 3.07234i 0.0192824 + 0.118167i
\(677\) 8.46874 14.6683i 0.325480 0.563748i −0.656129 0.754649i \(-0.727807\pi\)
0.981609 + 0.190900i \(0.0611407\pi\)
\(678\) −0.992083 0.839398i −0.0381007 0.0322369i
\(679\) 20.2031 11.6642i 0.775323 0.447633i
\(680\) −9.71478 0.186238i −0.372545 0.00714191i
\(681\) −34.7296 19.9449i −1.33084 0.764291i
\(682\) −0.707797 1.98401i −0.0271029 0.0759716i
\(683\) 2.98462i 0.114203i 0.998368 + 0.0571017i \(0.0181859\pi\)
−0.998368 + 0.0571017i \(0.981814\pi\)
\(684\) −6.08013 + 5.01762i −0.232480 + 0.191853i
\(685\) 8.64828i 0.330434i
\(686\) −23.2675 + 8.30071i −0.888358 + 0.316923i
\(687\) 11.0129 6.39209i 0.420169 0.243873i
\(688\) 37.5210 + 33.1542i 1.43047 + 1.26399i
\(689\) 47.1986 27.2501i 1.79812 1.03815i
\(690\) −10.2778 1.85564i −0.391268 0.0706432i
\(691\) 4.17425 7.23001i 0.158796 0.275043i −0.775639 0.631177i \(-0.782572\pi\)
0.934435 + 0.356134i \(0.115905\pi\)
\(692\) 6.64593 + 40.7277i 0.252640 + 1.54823i
\(693\) 13.1074 + 22.4638i 0.497911 + 0.853328i
\(694\) −18.6950 15.8916i −0.709653 0.603238i
\(695\) −4.72886 + 8.19062i −0.179376 + 0.310688i
\(696\) −2.28476 + 1.26820i −0.0866036 + 0.0480711i
\(697\) 19.7894 + 34.2762i 0.749577 + 1.29830i
\(698\) 2.14361 11.7187i 0.0811370 0.443559i
\(699\) −0.0822543 35.8044i −0.00311114 1.35425i
\(700\) −1.96567 + 5.19318i −0.0742954 + 0.196284i
\(701\) 9.37518 0.354096 0.177048 0.984202i \(-0.443345\pi\)
0.177048 + 0.984202i \(0.443345\pi\)
\(702\) 21.4863 + 18.0108i 0.810949 + 0.679773i
\(703\) 2.97267i 0.112117i
\(704\) 0.957431 24.9621i 0.0360845 0.940796i
\(705\) −5.29000 + 0.0121528i −0.199233 + 0.000457703i
\(706\) −4.39113 + 24.0054i −0.165262 + 0.903455i
\(707\) −5.34107 + 3.08367i −0.200872 + 0.115973i
\(708\) −12.5142 + 33.2925i −0.470313 + 1.25121i
\(709\) 33.2487 + 19.1962i 1.24868 + 0.720927i 0.970847 0.239702i \(-0.0770496\pi\)
0.277836 + 0.960629i \(0.410383\pi\)
\(710\) −7.22273 + 8.49686i −0.271064 + 0.318881i
\(711\) 0.563103 + 0.321667i 0.0211180 + 0.0120635i
\(712\) −7.04469 + 11.6789i −0.264011 + 0.437686i
\(713\) −1.76137 1.01693i −0.0659639 0.0380843i
\(714\) 22.9909 + 4.15099i 0.860412 + 0.155347i
\(715\) 5.95675 + 10.3174i 0.222770 + 0.385848i
\(716\) 9.50404 + 11.6250i 0.355183 + 0.434446i
\(717\) 4.01854 + 6.92354i 0.150075 + 0.258564i
\(718\) −3.38843 9.49802i −0.126455 0.354463i
\(719\) 12.8804 0.480356 0.240178 0.970729i \(-0.422794\pi\)
0.240178 + 0.970729i \(0.422794\pi\)
\(720\) 11.3599 3.86697i 0.423357 0.144114i
\(721\) 41.0138 1.52744
\(722\) −8.20830 23.0085i −0.305481 0.856287i
\(723\) 17.3997 30.2977i 0.647103 1.12679i
\(724\) −19.2601 23.5582i −0.715795 0.875533i
\(725\) −0.266702 0.461941i −0.00990505 0.0171561i
\(726\) −1.97710 + 2.33673i −0.0733770 + 0.0867241i
\(727\) −3.75846 2.16995i −0.139393 0.0804788i 0.428681 0.903456i \(-0.358978\pi\)
−0.568075 + 0.822977i \(0.692312\pi\)
\(728\) −25.6548 15.4749i −0.950830 0.573538i
\(729\) 26.9974 0.372154i 0.999905 0.0137835i
\(730\) −7.25938 + 8.53998i −0.268682 + 0.316079i
\(731\) 37.2407 + 21.5009i 1.37740 + 0.795241i
\(732\) 42.2684 6.99708i 1.56229 0.258619i
\(733\) −18.8815 + 10.9012i −0.697404 + 0.402646i −0.806380 0.591398i \(-0.798576\pi\)
0.108976 + 0.994044i \(0.465243\pi\)
\(734\) −8.63232 + 47.1911i −0.318625 + 1.74186i
\(735\) 0.610920 1.06378i 0.0225341 0.0392381i
\(736\) −14.9055 18.9622i −0.549423 0.698956i
\(737\) 21.7297i 0.800425i
\(738\) −37.3878 31.4866i −1.37626 1.15904i
\(739\) −31.8843 −1.17288 −0.586441 0.809992i \(-0.699471\pi\)
−0.586441 + 0.809992i \(0.699471\pi\)
\(740\) −1.60188 + 4.23207i −0.0588864 + 0.155574i
\(741\) 7.50917 4.35845i 0.275856 0.160112i
\(742\) −10.0921 + 55.1717i −0.370494 + 2.02542i
\(743\) −12.2533 21.2234i −0.449532 0.778612i 0.548824 0.835938i \(-0.315076\pi\)
−0.998355 + 0.0573263i \(0.981742\pi\)
\(744\) 2.33655 + 0.0394236i 0.0856622 + 0.00144534i
\(745\) 5.42917 9.40360i 0.198909 0.344521i
\(746\) −10.5513 8.96912i −0.386312 0.328383i
\(747\) −23.6552 13.5128i −0.865497 0.494407i
\(748\) −3.45516 21.1740i −0.126333 0.774197i
\(749\) −19.5395 + 33.8434i −0.713957 + 1.23661i
\(750\) 0.828349 + 2.30518i 0.0302470 + 0.0841731i
\(751\) 5.51362 3.18329i 0.201195 0.116160i −0.396018 0.918243i \(-0.629608\pi\)
0.597213 + 0.802083i \(0.296275\pi\)
\(752\) −9.15485 8.08938i −0.333843 0.294989i
\(753\) 0.0606699 + 26.4089i 0.00221093 + 0.962395i
\(754\) 2.71072 0.967053i 0.0987186 0.0352180i
\(755\) 10.8268i 0.394029i
\(756\) −28.4436 + 4.84290i −1.03448 + 0.176134i
\(757\) 25.0713i 0.911232i 0.890176 + 0.455616i \(0.150581\pi\)
−0.890176 + 0.455616i \(0.849419\pi\)
\(758\) 7.57702 + 21.2390i 0.275210 + 0.771434i
\(759\) −0.0529763 23.0600i −0.00192292 0.837024i
\(760\) 0.0712281 3.71548i 0.00258371 0.134775i
\(761\) 11.3876 6.57465i 0.412801 0.238331i −0.279191 0.960235i \(-0.590066\pi\)
0.691993 + 0.721905i \(0.256733\pi\)
\(762\) −1.27903 + 0.459611i −0.0463345 + 0.0166500i
\(763\) −22.9152 + 39.6903i −0.829587 + 1.43689i
\(764\) 4.38125 + 26.8492i 0.158508 + 0.971371i
\(765\) 8.90147 5.19394i 0.321833 0.187787i
\(766\) −6.78093 + 7.97713i −0.245005 + 0.288225i
\(767\) 19.5863 33.9245i 0.707221 1.22494i
\(768\) 25.5480 + 10.7378i 0.921883 + 0.387468i
\(769\) −11.6041 20.0990i −0.418456 0.724787i 0.577329 0.816512i \(-0.304095\pi\)
−0.995784 + 0.0917252i \(0.970762\pi\)
\(770\) −12.0603 2.20609i −0.434622 0.0795021i
\(771\) −2.15431 + 1.25040i −0.0775856 + 0.0450321i
\(772\) 41.5093 + 15.7117i 1.49395 + 0.565477i
\(773\) 32.0701 1.15348 0.576740 0.816928i \(-0.304325\pi\)
0.576740 + 0.816928i \(0.304325\pi\)
\(774\) −52.2840 9.31587i −1.87931 0.334852i
\(775\) 0.477015i 0.0171349i
\(776\) 20.8058 11.4863i 0.746886 0.412333i
\(777\) 5.41843 9.43498i 0.194385 0.338478i
\(778\) −36.1753 6.61727i −1.29695 0.237241i
\(779\) −13.1092 + 7.56858i −0.469685 + 0.271172i
\(780\) −13.0391 + 2.15849i −0.466876 + 0.0772862i
\(781\) −21.3243 12.3116i −0.763043 0.440543i
\(782\) −15.7827 13.4161i −0.564389 0.479757i
\(783\) 1.36925 2.40981i 0.0489329 0.0861196i
\(784\) 2.68604 0.900595i 0.0959299 0.0321641i
\(785\) 14.2718 + 8.23981i 0.509381 + 0.294091i
\(786\) −11.2657 9.53190i −0.401835 0.339992i
\(787\) 20.0375 + 34.7059i 0.714258 + 1.23713i 0.963245 + 0.268624i \(0.0865690\pi\)
−0.248987 + 0.968507i \(0.580098\pi\)
\(788\) 9.09109 7.43245i 0.323857 0.264770i
\(789\) 3.81031 6.63481i 0.135651 0.236205i
\(790\) −0.287932 + 0.102720i −0.0102442 + 0.00365462i
\(791\) −1.47297 −0.0523727
\(792\) 12.9121 + 23.1367i 0.458812 + 0.822126i
\(793\) −47.1872 −1.67567
\(794\) 35.8357 12.7844i 1.27176 0.453703i
\(795\) 12.4201 + 21.3985i 0.440495 + 0.758927i
\(796\) −22.1137 27.0487i −0.783800 0.958714i
\(797\) 28.1638 + 48.7811i 0.997612 + 1.72791i 0.558622 + 0.829423i \(0.311330\pi\)
0.438990 + 0.898492i \(0.355336\pi\)
\(798\) −1.58757 + 8.79301i −0.0561995 + 0.311269i
\(799\) −9.08646 5.24607i −0.321456 0.185593i
\(800\) −2.10356 + 5.25119i −0.0743722 + 0.185658i
\(801\) −0.0664679 14.4663i −0.00234853 0.511141i
\(802\) −11.2469 9.56042i −0.397143 0.337590i
\(803\) −21.4325 12.3741i −0.756337 0.436671i
\(804\) 22.5650 + 8.48189i 0.795808 + 0.299133i
\(805\) −10.2517 + 5.91884i −0.361326 + 0.208612i
\(806\) −2.53179 0.463122i −0.0891786 0.0163128i
\(807\) 43.1824 0.0992039i 1.52009 0.00349214i
\(808\) −5.50043 + 3.03662i −0.193504 + 0.106828i
\(809\) 17.2021i 0.604793i 0.953182 + 0.302397i \(0.0977867\pi\)
−0.953182 + 0.302397i \(0.902213\pi\)
\(810\) −8.15402 + 9.77302i −0.286503 + 0.343389i
\(811\) −56.3100 −1.97731 −0.988656 0.150196i \(-0.952010\pi\)
−0.988656 + 0.150196i \(0.952010\pi\)
\(812\) −1.04850 + 2.77006i −0.0367950 + 0.0972101i
\(813\) −0.0855761 37.2503i −0.00300128 1.30643i
\(814\) −9.82825 1.79781i −0.344480 0.0630132i
\(815\) 3.77957 + 6.54641i 0.132393 + 0.229311i
\(816\) 23.3366 + 4.67697i 0.816944 + 0.163727i
\(817\) −8.22317 + 14.2430i −0.287692 + 0.498298i
\(818\) −3.83579 + 4.51245i −0.134115 + 0.157774i
\(819\) 31.7777 0.146008i 1.11040 0.00510194i
\(820\) 22.7414 3.71094i 0.794165 0.129592i
\(821\) 1.37477 2.38117i 0.0479797 0.0831033i −0.841038 0.540976i \(-0.818055\pi\)
0.889018 + 0.457873i \(0.151388\pi\)
\(822\) 3.76388 20.8468i 0.131280 0.727117i
\(823\) 23.4482 13.5378i 0.817353 0.471899i −0.0321498 0.999483i \(-0.510235\pi\)
0.849503 + 0.527584i \(0.176902\pi\)
\(824\) 41.7751 + 0.800855i 1.45531 + 0.0278991i
\(825\) −4.67762 + 2.71497i −0.162854 + 0.0945231i
\(826\) 13.5456 + 37.9693i 0.471312 + 1.32112i
\(827\) 29.3670i 1.02119i 0.859821 + 0.510596i \(0.170575\pi\)
−0.859821 + 0.510596i \(0.829425\pi\)
\(828\) 23.9671 + 8.94612i 0.832914 + 0.310899i
\(829\) 30.1503i 1.04716i −0.851975 0.523582i \(-0.824595\pi\)
0.851975 0.523582i \(-0.175405\pi\)
\(830\) 12.0956 4.31513i 0.419846 0.149780i
\(831\) 1.20209 + 0.690350i 0.0417001 + 0.0239480i
\(832\) −25.8288 16.2631i −0.895453 0.563821i
\(833\) 2.10710 1.21653i 0.0730066 0.0421504i
\(834\) 14.9637 17.6855i 0.518150 0.612400i
\(835\) −10.6372 + 18.4242i −0.368115 + 0.637594i
\(836\) 8.09812 1.32145i 0.280079 0.0457033i
\(837\) −2.13797 + 1.25409i −0.0738992 + 0.0433475i
\(838\) 3.49480 + 2.97074i 0.120726 + 0.102623i
\(839\) 3.81222 6.60296i 0.131612 0.227959i −0.792686 0.609630i \(-0.791318\pi\)
0.924298 + 0.381671i \(0.124651\pi\)
\(840\) 6.99845 11.6627i 0.241469 0.402403i
\(841\) 14.3577 + 24.8683i 0.495094 + 0.857529i
\(842\) −1.60297 + 8.76313i −0.0552422 + 0.301997i
\(843\) 30.8804 + 17.7343i 1.06358 + 0.610803i
\(844\) 32.9371 + 12.4670i 1.13374 + 0.429133i
\(845\) 1.55649 0.0535448
\(846\) 12.7569 + 2.27300i 0.438592 + 0.0781475i
\(847\) 3.46939i 0.119210i
\(848\) −11.3568 + 55.9987i −0.389993 + 1.92300i
\(849\) −12.7313 21.9348i −0.436938 0.752799i
\(850\) −0.874185 + 4.77899i −0.0299843 + 0.163918i
\(851\) −8.35443 + 4.82343i −0.286386 + 0.165345i
\(852\) 21.1085 17.3384i 0.723164 0.594002i
\(853\) −19.9923 11.5426i −0.684525 0.395211i 0.117033 0.993128i \(-0.462662\pi\)
−0.801558 + 0.597917i \(0.795995\pi\)
\(854\) 31.4515 36.9998i 1.07625 1.26611i
\(855\) 1.98646 + 3.40442i 0.0679354 + 0.116429i
\(856\) −20.5630 + 34.0900i −0.702829 + 1.16517i
\(857\) 0.537623 + 0.310397i 0.0183649 + 0.0106030i 0.509154 0.860675i \(-0.329958\pi\)
−0.490789 + 0.871278i \(0.663292\pi\)
\(858\) −9.86853 27.4627i −0.336906 0.937561i
\(859\) −12.4175 21.5077i −0.423678 0.733833i 0.572618 0.819823i \(-0.305928\pi\)
−0.996296 + 0.0859901i \(0.972595\pi\)
\(860\) 19.3821 15.8459i 0.660923 0.540340i
\(861\) −55.4028 + 0.127278i −1.88812 + 0.00433763i
\(862\) 8.07136 + 22.6246i 0.274912 + 0.770598i
\(863\) −2.55660 −0.0870275 −0.0435138 0.999053i \(-0.513855\pi\)
−0.0435138 + 0.999053i \(0.513855\pi\)
\(864\) −29.0661 + 4.37739i −0.988849 + 0.148922i
\(865\) 20.6332 0.701549
\(866\) −8.38833 23.5131i −0.285047 0.799008i
\(867\) −9.00410 + 0.0206853i −0.305795 + 0.000702511i
\(868\) 2.05064 1.67651i 0.0696034 0.0569045i
\(869\) −0.337498 0.584563i −0.0114488 0.0198299i
\(870\) 0.441844 + 1.22959i 0.0149799 + 0.0416870i
\(871\) −22.9934 13.2752i −0.779101 0.449814i
\(872\) −24.1156 + 39.9796i −0.816657 + 1.35388i
\(873\) −12.5033 + 21.8880i −0.423173 + 0.740798i
\(874\) 5.13106 6.03621i 0.173561 0.204178i
\(875\) 2.40441 + 1.38819i 0.0812839 + 0.0469293i
\(876\) 21.2156 17.4263i 0.716808 0.588782i
\(877\) −14.8560 + 8.57713i −0.501653 + 0.289629i −0.729396 0.684092i \(-0.760199\pi\)
0.227743 + 0.973721i \(0.426865\pi\)
\(878\) 9.74360 53.2662i 0.328830 1.79765i
\(879\) 23.3743 + 40.2715i 0.788396 + 1.35832i
\(880\) −12.2410 2.48254i −0.412646 0.0836863i
\(881\) 0.662030i 0.0223043i 0.999938 + 0.0111522i \(0.00354992\pi\)
−0.999938 + 0.0111522i \(0.996450\pi\)
\(882\) −1.93561 + 2.29838i −0.0651753 + 0.0773904i
\(883\) −11.4683 −0.385939 −0.192969 0.981205i \(-0.561812\pi\)
−0.192969 + 0.981205i \(0.561812\pi\)
\(884\) −24.5161 9.27961i −0.824567 0.312107i
\(885\) 15.4213 + 8.85630i 0.518380 + 0.297701i
\(886\) 3.33548 18.2344i 0.112058 0.612596i
\(887\) −23.5408 40.7738i −0.790422 1.36905i −0.925706 0.378245i \(-0.876528\pi\)
0.135283 0.990807i \(-0.456806\pi\)
\(888\) 5.70323 9.50431i 0.191388 0.318944i
\(889\) −0.770239 + 1.33409i −0.0258330 + 0.0447440i
\(890\) 5.19596 + 4.41681i 0.174169 + 0.148052i
\(891\) −24.4660 13.8273i −0.819643 0.463231i
\(892\) −16.9064 + 2.75879i −0.566069 + 0.0923710i
\(893\) 2.00639 3.47518i 0.0671414 0.116292i
\(894\) −17.1797 + 20.3047i −0.574576 + 0.679089i
\(895\) 6.50193 3.75389i 0.217335 0.125479i
\(896\) 29.9676 9.41275i 1.00115 0.314458i
\(897\) −24.4333 14.0318i −0.815805 0.468510i
\(898\) −33.2276 + 11.8540i −1.10882 + 0.395573i
\(899\) 0.254441i 0.00848609i
\(900\) −0.993496 5.91718i −0.0331165 0.197239i
\(901\) 49.0725i 1.63484i
\(902\) 17.0951 + 47.9188i 0.569204 + 1.59552i
\(903\) −52.0608 + 30.2170i −1.73248 + 1.00556i
\(904\) −1.50031 0.0287619i −0.0498996 0.000956605i
\(905\) −13.1762 + 7.60731i −0.437993 + 0.252876i
\(906\) −4.71202 + 26.0982i −0.156546 + 0.867056i
\(907\) 5.68246 9.84232i 0.188683 0.326809i −0.756128 0.654423i \(-0.772911\pi\)
0.944811 + 0.327615i \(0.106245\pi\)
\(908\) −45.6413 + 7.44773i −1.51466 + 0.247162i
\(909\) 3.30550 5.78653i 0.109636 0.191927i
\(910\) −9.70229 + 11.4138i −0.321628 + 0.378365i
\(911\) −0.698984 + 1.21068i −0.0231584 + 0.0401115i −0.877372 0.479810i \(-0.840706\pi\)
0.854214 + 0.519922i \(0.174039\pi\)
\(912\) −1.78874 + 8.92523i −0.0592310 + 0.295544i
\(913\) 14.1778 + 24.5567i 0.469217 + 0.812708i
\(914\) 36.9419 + 6.75751i 1.22193 + 0.223519i
\(915\) −0.0492127 21.4218i −0.00162692 0.708182i
\(916\) 5.20502 13.7513i 0.171979 0.454356i
\(917\) −16.7265 −0.552358
\(918\) −23.7176 + 8.64601i −0.782798 + 0.285361i
\(919\) 7.89210i 0.260336i 0.991492 + 0.130168i \(0.0415517\pi\)
−0.991492 + 0.130168i \(0.958448\pi\)
\(920\) −10.5576 + 5.82852i −0.348074 + 0.192161i
\(921\) 37.0379 0.0850880i 1.22044 0.00280374i
\(922\) −16.6855 3.05215i −0.549507 0.100517i
\(923\) −26.0551 + 15.0429i −0.857612 + 0.495143i
\(924\) 28.1113 + 10.5667i 0.924795 + 0.347618i
\(925\) 1.95942 + 1.13127i 0.0644254 + 0.0371960i
\(926\) 27.2560 + 23.1689i 0.895688 + 0.761377i
\(927\) −38.2777 + 22.3348i −1.25721 + 0.733571i
\(928\) −1.12205 + 2.80100i −0.0368330 + 0.0919475i
\(929\) −15.9015 9.18072i −0.521710 0.301210i 0.215924 0.976410i \(-0.430724\pi\)
−0.737634 + 0.675201i \(0.764057\pi\)
\(930\) 0.207605 1.14985i 0.00680764 0.0377051i
\(931\) 0.465271 + 0.805873i 0.0152486 + 0.0264114i
\(932\) −26.1682 32.0079i −0.857168 1.04845i
\(933\) 18.6141 + 32.0702i 0.609399 + 1.04993i
\(934\) −9.91039 + 3.53554i −0.324278 + 0.115687i
\(935\) −10.7270 −0.350811
\(936\) 32.3704 + 0.471788i 1.05806 + 0.0154209i
\(937\) −11.5833 −0.378411 −0.189205 0.981938i \(-0.560591\pi\)
−0.189205 + 0.981938i \(0.560591\pi\)
\(938\) 25.7349 9.18095i 0.840274 0.299769i
\(939\) −5.03432 + 8.76614i −0.164289 + 0.286072i
\(940\) −4.72908 + 3.86628i −0.154246 + 0.126104i
\(941\) −2.75857 4.77799i −0.0899270 0.155758i 0.817553 0.575853i \(-0.195330\pi\)
−0.907480 + 0.420095i \(0.861997\pi\)
\(942\) −30.8162 26.0735i −1.00405 0.849521i
\(943\) 42.5416 + 24.5614i 1.38534 + 0.799829i
\(944\) 13.0556 + 38.9386i 0.424924 + 1.26734i
\(945\) 0.0994258 + 14.4261i 0.00323432 + 0.469282i
\(946\) 42.1168 + 35.8013i 1.36934 + 1.16400i
\(947\) −14.0517 8.11276i −0.456620 0.263629i 0.254002 0.967204i \(-0.418253\pi\)
−0.710622 + 0.703574i \(0.751586\pi\)
\(948\) 0.738771 0.122296i 0.0239942 0.00397198i
\(949\) −26.1873 + 15.1192i −0.850075 + 0.490791i
\(950\) −1.82775 0.334338i −0.0593002 0.0108473i
\(951\) −7.22951 + 12.5886i −0.234433 + 0.408212i
\(952\) 23.6169 13.0381i 0.765427 0.422569i
\(953\) 0.197221i 0.00638861i −0.999995 0.00319431i \(-0.998983\pi\)
0.999995 0.00319431i \(-0.00101678\pi\)
\(954\) −20.6258 56.9869i −0.667784 1.84502i
\(955\) 13.6022 0.440156
\(956\) 8.64510 + 3.27226i 0.279603 + 0.105832i
\(957\) −2.49506 + 1.44817i −0.0806537 + 0.0468128i
\(958\) −54.4584 9.96168i −1.75947 0.321847i
\(959\) −12.0054 20.7940i −0.387676 0.671474i
\(960\) 7.35608 11.7426i 0.237417 0.378990i
\(961\) −15.3862 + 26.6497i −0.496330 + 0.859669i
\(962\) −7.90667 + 9.30146i −0.254921 + 0.299891i
\(963\) −0.194015 42.2262i −0.00625206 1.36072i
\(964\) −6.49732 39.8170i −0.209265 1.28242i
\(965\) 11.0958 19.2185i 0.357188 0.618667i
\(966\) 27.2879 9.80573i 0.877975 0.315494i
\(967\) −21.8675 + 12.6252i −0.703213 + 0.406000i −0.808543 0.588437i \(-0.799743\pi\)
0.105330 + 0.994437i \(0.466410\pi\)
\(968\) −0.0677450 + 3.53379i −0.00217741 + 0.113580i
\(969\) 0.0179597 + 7.81767i 0.000576949 + 0.251140i
\(970\) −3.99278 11.1921i −0.128200 0.359355i
\(971\) 10.6137i 0.340610i −0.985391 0.170305i \(-0.945525\pi\)
0.985391 0.170305i \(-0.0544753\pi\)
\(972\) 23.9088 20.0093i 0.766874 0.641797i
\(973\) 26.2581i 0.841798i
\(974\) 26.7403 9.53965i 0.856816 0.305670i
\(975\) 0.0151813 + 6.60827i 0.000486192 + 0.211634i
\(976\) 32.7578 37.0724i 1.04855 1.18666i
\(977\) −24.4452 + 14.1134i −0.782071 + 0.451529i −0.837164 0.546952i \(-0.815788\pi\)
0.0550925 + 0.998481i \(0.482455\pi\)
\(978\) −6.26161 17.4252i −0.200224 0.557195i
\(979\) −7.52873 + 13.0401i −0.240619 + 0.416765i
\(980\) −0.228127 1.39801i −0.00728724 0.0446577i
\(981\) −0.227535 49.5214i −0.00726462 1.58110i
\(982\) 22.8385 + 19.4138i 0.728806 + 0.619519i
\(983\) −22.5114 + 38.9908i −0.718001 + 1.24361i 0.243790 + 0.969828i \(0.421609\pi\)
−0.961791 + 0.273786i \(0.911724\pi\)
\(984\) −56.4337 0.952179i −1.79904 0.0303544i
\(985\) −2.93566 5.08471i −0.0935378 0.162012i
\(986\) −0.466293 + 2.54913i −0.0148498 + 0.0811808i
\(987\) 12.7025 7.37273i 0.404324 0.234677i
\(988\) 3.54905 9.37635i 0.112910 0.298301i
\(989\) 53.3713 1.69711
\(990\) 12.4571 4.50870i 0.395912 0.143296i
\(991\) 45.4039i 1.44230i −0.692778 0.721151i \(-0.743613\pi\)
0.692778 0.721151i \(-0.256387\pi\)
\(992\) 2.12144 1.66759i 0.0673559 0.0529460i
\(993\) 1.55457 2.70694i 0.0493328 0.0859020i
\(994\) 5.57117 30.4564i 0.176707 0.966019i
\(995\) −15.1285 + 8.73444i −0.479605 + 0.276900i
\(996\) −31.0348 + 5.13747i −0.983374 + 0.162787i
\(997\) 15.3295 + 8.85052i 0.485492 + 0.280299i 0.722702 0.691160i \(-0.242900\pi\)
−0.237211 + 0.971458i \(0.576233\pi\)
\(998\) 7.45715 8.77263i 0.236052 0.277693i
\(999\) 0.0810249 + 11.7563i 0.00256351 + 0.371951i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 360.2.bm.b.11.15 yes 48
3.2 odd 2 1080.2.bm.a.251.10 48
4.3 odd 2 1440.2.cc.b.911.24 48
8.3 odd 2 360.2.bm.a.11.24 48
8.5 even 2 1440.2.cc.a.911.24 48
9.4 even 3 1080.2.bm.b.611.1 48
9.5 odd 6 360.2.bm.a.131.24 yes 48
12.11 even 2 4320.2.cc.a.1871.19 48
24.5 odd 2 4320.2.cc.b.1871.6 48
24.11 even 2 1080.2.bm.b.251.1 48
36.23 even 6 1440.2.cc.a.1391.24 48
36.31 odd 6 4320.2.cc.b.3311.6 48
72.5 odd 6 1440.2.cc.b.1391.24 48
72.13 even 6 4320.2.cc.a.3311.19 48
72.59 even 6 inner 360.2.bm.b.131.15 yes 48
72.67 odd 6 1080.2.bm.a.611.10 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
360.2.bm.a.11.24 48 8.3 odd 2
360.2.bm.a.131.24 yes 48 9.5 odd 6
360.2.bm.b.11.15 yes 48 1.1 even 1 trivial
360.2.bm.b.131.15 yes 48 72.59 even 6 inner
1080.2.bm.a.251.10 48 3.2 odd 2
1080.2.bm.a.611.10 48 72.67 odd 6
1080.2.bm.b.251.1 48 24.11 even 2
1080.2.bm.b.611.1 48 9.4 even 3
1440.2.cc.a.911.24 48 8.5 even 2
1440.2.cc.a.1391.24 48 36.23 even 6
1440.2.cc.b.911.24 48 4.3 odd 2
1440.2.cc.b.1391.24 48 72.5 odd 6
4320.2.cc.a.1871.19 48 12.11 even 2
4320.2.cc.a.3311.19 48 72.13 even 6
4320.2.cc.b.1871.6 48 24.5 odd 2
4320.2.cc.b.3311.6 48 36.31 odd 6